The student pilot stated he was performing a short field landing to runway 14 during his flight examination. Approximately 50 feet above ground level it was apparent to the pilot that he was not going to land on his intended touchdown point, and the flight examiner in the right seat directed the pilot to go-around. The student pilot applied full power, however, the airplane “landed hard” before becoming airborne again. The flight examiner took over the flight controls and successfully landed the airplane. An examination of the airplane revealed that the firewall was wrinkled, the nose gear bent, and the fuselage skin aft of the nose gear was wrinkled. The pilot and examiner were not injured. The pilot reported that there were no mechanical anomalies with the airplane and that weather was not a contributing factor.